Running head: IMPROVING ACHIEVEMENT IN MATHEMATICS
Improving Mathematics Achievement in the United States: Heterogeneous Grouping and the
Role of the International Baccalaureate Curriculum
Jacob West
Vanderbilt University
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IMPROVING ACHIEVEMENT IN MATHEMATICS
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Abstract
Both national and international assessments show that U.S. students exhibit many areas in
need of improvement for mathematics achievement. Of these, the mathematic content of algebra
consistently proves to be a challenge to U.S. students in 8th grade or at 15 years-old. One
obstacle for many students in achieving high levels in mathematics is a lack of access to an
Algebra I course by 8th grade. Homogenous grouping systems used in many middle schools
limits students’ class options and thus potential mathematics coursework and achievement in
high-school and beyond .This paper proposes to improve mathematics achievement and
outcomes for all students but focusing on the middle school years (sixth to eighth grade) and the
importance of heterogeneous grouping of students during that time period. Additionally, as all
students benefit from heterogeneous grouping with high-level curriculum, they enter high-school
with higher levels of math readiness which necessitate rigorous mathematics curricula. To
maximize student achievement and outcomes in high-school, it is suggested that schools
continue heterogeneous grouping of students in International Baccalaureate Diploma Program
coursework, which offers students an opportunity to improve mathematics achievement as well
as the likelihood of entering and completing post-secondary education.
Keywords: mathematics achievement, heterogeneous grouping, International Baccalaureate
IMPROVING ACHIEVEMENT IN MATHEMATICS
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Improving Mathematics Achievement in the United States: Heterogeneous Grouping and the
Role of the International Baccalaureate Curriculum
This initial study began by looking at various nations with the hope of comparing
the educational achievement in mathematics across countries for insight as to the impact of the
International Baccalaureate Diploma Program (IBDP) upon achievement. However, in analyzing
the various chosen pieces of mathematics achievement data it became obvious that although the
United States contains more schools with the IBDP and produces more diploma candidates in
gross numbers (International Baccalaureate Organization, 2011) the overall scores in
mathematics achievement for the United States have remained fairly static and low. This fact led
to a focus on the most recent national and international assessments of mathematics for students
of the United States with the hope of finding traits that could be altered or controlled within
schools in order to improve student achievement in mathematics through grouping practices and
specific curriculum in middle school and high school.
What Do Assessments Show Regarding U.S. Mathematics Achievement?
Within the education system of the United States, attaining above average and high
achievement in mathematics remains a challenge for the vast majority of students. International
assessments such as Trends in International Mathematics and Science Study (TIMSS) and the
Programme for International Student Assessment (PISA) provide evidence of the levels of
achievement in several content areas; however this review focuses upon the reported results of
student performance in the area of mathematics as measured by these assessments. TIMSS
assessed both 4th-grade and 8th-grade students, but only the 8th-grade scores will be discussed
here. Additionally, PISA assesses 15-year-old students across the world for both reading and
IMPROVING ACHIEVEMENT IN MATHEMATICS
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mathematics. Though some grade levels may differ by country for this particular age, in the
United States the majority of students at this age are in either 8th or 9th grade. Both of these
assessments measure mathematics achievement at a critical stage for students and they likely
indicate students’ achievement levels in mathematics at the beginning of their high-school
careers.
TIMSS specifically test achievement levels related directly to mathematical topics and
skills, and for 8th grade mathematics the domains are: numbers, algebra, geometry, and data and
chance. The average score for the United States in mathematics, according to TIMSS 2007,
places U.S. students below the average scores of students of Chinese Taipei, the Republic of
Korea, Singapore, Hong Kong, and Japan, while Hungary, England, Russian Federation,
Lithuania, and Czech Republic all scored averages with statistically insignificant differences
from the United States (Provasnick & Gonzales, 2009). In the specific content domains, U.S.
8th-grade students’ average scores exceeded the TIMSS 2007 scaled average only in the areas of
numbers and data /chance. These content scores indicate that both algebra and geometry were
shown to be the weakest areas for U.S. students of the four being assessed (Gonzales et al.,
2008). Therefore, the contents of algebra and geometry in the TIMSS 2007 represent areas which
nee improvement in U.S. mathematics achievement for students entering high-school.
Differing from TIMMS in what it tests, PISA assesses mathematics literacy, which is
defined by the Organization for Economic Cooperation and Development (OECD) as
An individual’s capacity to identify and understand the role that mathematics plays in the
world, to make well founded judgments and to use and engage with mathematics in ways
IMPROVING ACHIEVEMENT IN MATHEMATICS
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that meet the needs of that individual’s life as a constructive, concerned, and reflective
citizen. (Organization for Economic Cooperation and Development, 2006, p. 12)
This mathematics literacy requires students to go beyond simply showing content knowledge and
skills, but to additionally apply mathematical knowledge. In PISA 2006, the average scores for
mathematics literacy of 15-year-old students of the United States were below the OECD average.
This placed the U.S. behind 23 of 29 OECD countries as well as behind 8 of27 non-OECD
countries in mathematics literacy (Provasnick & Gonzales, 2009). Though some scores
improved slightly in the last several years, PISA rankings for the United States remain at similar
levels in comparison to other countries, keeping the United States ranked outside of the top
twenty in the world in regards to mathematics literacy (Organization for Economic Cooperation
and Development, 2010). Furthermore, when comparing only the top 10 percent of student
performance for PISA 2006 by jurisdiction, 29 of the same 31 nations that performed above the
U.S in overall average score also scored higher than the students in the top 10 percent from the
United States (Provasnick & Gonzales, 2009). These performances are unacceptably low for the
United States and raise concerns for students’ mathematical understanding and application.
Additionally, the low performances mandate specific attention to mathematics if the United
States seeks to produce highly educated students who show the capability of maximizing their
own opportunities through high levels of preparedness beyond middle and high school.
One final assessment worth exploring is the National Assessment of Educational Progress
(NAEP). For 8th grade mathematics, this assessment tests a representative sample of students in
the content areas of number properties and operations, measurement, geometry, data
analysis/statistics and probability, and algebra. The latest results from a 2011 assessment show
that the average mathematics scores for 8th grade students increased by 1 point which showed a
IMPROVING ACHIEVEMENT IN MATHEMATICS
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statistically significant difference from the previous 2009 assessment (National Assessment of
Educational Progress, 2011). The results of this assessment also represent a trend of increases in
mathematics achievement from the initial testing in 1990, though there remain many reasons for
concern regarding the reported achievement in mathematics of specific groups of students. For
example, among 8th graders scoring below the 25th percentile for mathematics in 2011, 33%
identify as White, 28% Black, 32% Hispanic, and 2% Asian (National Assessment of
Educational Progress, 2011). Additionally, according to NAEP (2011), 68% of these students
scoring in the bottom quarter were identified as eligible for free/reduced lunch. In contrast, of the
students who scored above the 75th percentile, 72% identify as White, 5% Black, 11% Hispanic,
and 2% Asian (National Assessment of Educational Progress, 2011). Of these students, only 20%
were eligible for free/reduced lunch (National Assessment of Educational Progress, 2011). These
statistics indicate that students of color, specifically Black and Hispanic students, are
underrepresented in the highest achieving groups for mathematics while simultaneously
overrepresented in the lowest achieving group of students. Additionally, free/reduced lunch,
which serves as a measure of family income, indicates through these results that students from
low-income families underachieve at higher rates than any other group. Since 2003, the NAEP
assessment has been given every other year, and each year shows an increase in the percentage
of students identified as eligible for free lunch with the largest amount at 39% eligible in 2011
(National Assessment of Educational Progress, 2011). As the percentage grows, it is concerning
that “In 2011, eighth-graders who were eligible for free lunch scored 28 points lower on average
than those not eligible” (National Assessment of Educational Progress, 2011 p.44). Though
there may be several factors that contribute to the low performances of minority students and
students eligible for free/reduced lunch, these statistics demand attention and action. Educators
IMPROVING ACHIEVEMENT IN MATHEMATICS
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must initiate specific interventions now in order to see improvement in mathematics achievement
within the United States for all student groups. The issue exhibits elements of the challenges of
equity as well as achievement and it requires intervention if the United States expects the results
to change.
Identifying a Starting Point for Intervention
As each of these assessments of 8th grade or 15-year-old students was examined, some
similarities in assessments became obvious. One such area is the mathematic content of algebra,
which both TIMSS and NAEP assessed directly. Discussed previously was the fact that
according to TIMSS both algebra and geometry remained the areas of lowest performance for
U.S. students in mathematics achievement. Additionally, NAEP identifies that of the five content
areas assessed for mathematics, algebra represents the largest portion with 30% of the total
mathematics questions being in the content area of algebra (National Assessment of Educational
Progress, 2011). However, according to NAEP in 2011 only 34% of the representative sample of
students was identified as taking Algebra I as their mathematics course for the school year, while
48% of students were taking general/basic 8th grade math or pre-algebra courses (National
Assessment of Educational Progress, 2011). Additionally, the results show that the students
taking an Algebra I course scored highest, followed by pre-algebra students, while the basic math
students scored the lowest on NAEP for mathematics achievement (National Assessment of
Educational Progress, 2011). NAEP identified the race/ethnicity of students taking various
courses which showed that “The percentages of students taking basic math courses were higher
for Black, Hispanic, and American Indian/Alaskan Native students than for White, Asian, and
multiracial students” (National Assessment of Educational Progress, 2011, p. 46). These pieces
of data hint at a point for intervention which exists within the U.S. education system as
IMPROVING ACHIEVEMENT IN MATHEMATICS
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coursework offerings and student groupings may be keeping many students from reaching their
highest potential in achievement of mathematics. Certainly, students of any background cannot
be expected to improve in mathematical achievement as measured by these assessments if they
do not have an opportunity to complete an algebra course when a large portion of the questions
assess algebraic understanding and skills. The NAEP data shows that students in 8th grade
complete various courses in mathematics and this variation in coursework likely is a results of
the practice of homogenous grouping that schools often practice, particularly beginning in
middle school for mathematics. The practice of grouping of students for mathematics based upon
prior achievement levels needs to be questioned and changes considered if achievement and
equity remain goals of education.
What Are the Implications of Grouping for Mathematical Achievement?
The debate about the benefits of homogenous and heterogeneous grouping of students
based upon prior achievement levels remains heated and research continues to this today.
Supporters of homogenous student grouping argue that low-track classes offer those students the
best opportunities to improve, while heterogeneous tracking limits the learning opportunities for
high-achieving students (Loveless, 1998). However, proponents of heterogeneous student
grouping argue that low-track placement with homogenous grouping perpetuates low
achievement levels (Heubert & Hauser 1999). The argument of proponents of heterogeneous
grouping proposes that often the best curriculum for all students is the same one that typically
used for only those high-achieving tracks of students (Burris, Heubert, & Levin, 2006).
However, giving all students the opportunity to achieve at high levels in mathematics in middle
schools requires that more students be given an opportunity to experience a rigorous algebra
curriculum early in their mathematics careers.
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Burris et al. (2006) conducted a longitudinal study of students in a New York school
district to identify the results of heterogeneously grouping students for high-achieving
mathematics courses during 6-8th grade. Students were identified by achievement levels for the
purpose of this study based upon fifth-grade scores according to the Iowa Test of Basic Skills
(ITBS), and then were followed through high-school graduation. Various outcomes measured for
the study included mathematics coursework completed as well as exam scores upon New York
State Board of Regents’ Sequential Mathematics I Regents Examination, and any scores upon
Advanced Placement Calculus Examinations taken by students. The results of the universally
accelerated 6-8th grade students were compared to the previous three years of results from
students who had experienced homogenous tracking in mathematics within the same schools.
The results of this study showed that:
The percentage of students taking advanced math courses did increase after universal
acceleration. More students took advanced mathematics classes, more students passed
such courses along with their associated New York state examinations, and more students
completed such courses a year or sooner than the average student in New York state.
(Burris, et al., 2006, p.117)
The results indicate that all students benefited from universal acceleration of mathematics,
including the highest-performing students. Additionally, results for specific sub-groups of
students showed that after universal acceleration in mathematics, the percentage of minority
students who passed the Sequential Mathematics I regents examination before high-school
increased from 23% to 75% (Burris et al., 2006). Though some opponents of heterogeneous
mathematics classrooms might argue that putting low-achieving students and high-achieving
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students in the same class creates an environment where the higher-achieving students suffer, the
data of this study suggests otherwise.
In addition to this study, a research meta-analysis of experimental ability grouping done
by Robert Slavin (1990) showed that homogenous grouping of students achieving at any level
(high, average, or low) had little effect on achievement, when the curriculum for comparisons
remains a constant. The significance of this is that schools implementing the same curriculum for
all students, such as algebra in 8th grade, increases students’ achievement levels as well as the
equity of opportunities for mathematics courses in high-school. Burris et al. (2006), Slavin
(1990), and Wheelock (1992) each recommended accelerated curriculum in mathematics for all
students via heterogeneous grouping in order to improve achievement, and have suggested that
schools begin the process of eliminating ability tracking in mathematics altogether. If schools
offer accelerated algebra curriculum by the end of middle school, all students will have the
option of choosing rigorous academic courses in high-school. To improve achievement, Burris et
al. (2008) and Wheelock (1992) propose that schools must exhibit a commitment to high
expectations for all students while providing equitable access to a rigorous curriculum. In
mathematics this means avoiding tracking and embracing a belief that all students possess the
capacity to reach high achievement levels and expecting that of students.
Additionally, to raise achievement for student and improve opportunities for all students
to be successful, heterogeneous and rigorous schooling must take place not only in middle
school, but in high school as well. If students’ achievement in mathematics at 8th grade reaches
levels of proficiency in the subject of algebra, advanced coursework completion in high school
becomes an option for all students. Students in homogenous settings for mathematics who are
placed in lower-achieving tracks are unlikely to complete an algebra course by the end of middle
IMPROVING ACHIEVEMENT IN MATHEMATICS
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school. This places these students at a disadvantage as it limits the levels of mathematic
coursework that a student could complete in high school. This means that though these students
may complete Geometry and Algebra II, they remain less likely to have the option of completing
a course in advanced mathematics (beyond requirements for high school graduation) such as
Trigonometry/Pre-Calculus and Calculus before graduation. However, if middle schools assist all
students in completing algebra by the end of 8th grade, then these students necessitate rigorous
mathematics curricula for continued high-achievement in mathematics. Having an advanced and
consistent mathematics curriculum for college preparedness must be a focus of high school
education. Thus, high schools need to consider what part they play in continuing highachievement levels in mathematics in order to maximize student outcomes.
What Role Could the International Baccalaureate Diploma Play in Student Outcomes?
The International Baccalaureate Organization (IBO) was originally created in 1967
through collaborative efforts of several international school educators in Switzerland and France.
The purpose of the design was in response to the needs of expatriate and internationally mobile
families who required a rigorous curriculum that would engage and prepare students for
university entrance. The original design included only the Diploma Program (DP), though since
then the IBO has expanded to create a specific program for elementary in the Primary Years
Program (PYP) and in middle school with the Middle Years Program (MYP). The DP was
created specifically for high school students with requirements for earning an IBDP, which
represents coursework above and beyond national requirements for high school graduation.
These requirements necessitate taking six courses with at least one in each of the content areas of
language, social studies, experimental sciences, mathematics, and arts. In addition to this,
students must complete an extended essay, which is essentially an extensive research paper.
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Finally, students must complete a Theory of Knowledge course designed to help students
understand more about learners and learning, as well as meet the required hours of community
service for Creativity, action, service (CAS) requirements (http://ibo.org/diploma). All of these
elements represent the minimum requirements, and the coursework requirements are typically
met during the junior and senior year of high school through classes with teachers trained for the
implementation of the IBDP curriculum.
The IB curriculum for mathematics includes three separate courses offered currently. The
IBDP offers Mathematics Studies Standard Level, Mathematics SL, and Mathematics Higher
Level as potential courses for students. The mathematics courses, though with different names
represent the equivalent of Algebra II (Mathematics Studies Standard Level), Trigonometry/PreCalculus (Mathematics SL), and Calculus (Mathematics Higher Level) in their content. The
Mathematics SL and Mathematics Higher Level represent advanced mathematics designed to
prepare students for engagement in university level coursework as they continue on in their
academic careers. These courses offer a continuum of rigor for academic achievement that must
begin with 8th grade algebra and continue into high school in order to offer these courses as
options for all students. However, this recommendation raises the question as to why schools
should choose IBDP over other curriculum as one which possesses the greatest potential for
continued improvement of academic achievement in mathematics.
The IBDP curriculum is already prevalent in many schools in the United States and
continues to expand, which is one reason for the recommendation of IBDP for this continuum
into high schools. In recent decades, the IBO has grown greatly in popularity and has been
adopted by many state schools in nations all over the world, none to a greater degree than the
United States. Since the inception of IBO, the program has gained notoriety as an advanced
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program which gives students an opportunity to prepare for university. Additionally, as schools
within the United States adopt the IBDP at high rates, the influence of the program continues to
increase yearly. The very first IBDP in the United States began in 1971 in New York and as of
2010 there are over 700 IBDP programs within the United States (International Baccalaureate
Organization, 2010b). Additionally, the United States leads all nations in number of all IBO
programs (PYP, MYP, and IBDP) offered with 1,207 schools using the programs. Of these U.S.
schools, 91% are public schools (International Baccalaureate Organization, 2010b). This trend of
adoption by public schools within the United States is significant as it offers the option of this
program to more students from a wider variety of diverse backgrounds within the United States
than ever before.
In addition to the increased accessibility of the IBDP in the United States, IBO offers
schools the chance to use IBO created external examinations for IB courses to assess students.
The IB exams taken by diploma candidates offer students an opportunity to earn college-credits
as many universities accept exam scores for credit hours, similar to the Advanced Placement
(AP) system created by College Board. Though AP classes have traditionally been the most
common in U.S. high schools, IB represents a more complete curriculum design focused on all
contents areas, as well as research and service. In comparison, AP is significantly cheaper and
simpler for schools to adopt (as schools have the option of adopting one course at a time),
whereas IB adoption includes a large financial commitment on the part of the school and a
dedication to professional development of teachers for the use of the IBO curriculum amongst
other things. The ease of adopting AP may be a reason for its traditionally greater popularity
among some high-schools. However, the IB curriculum for mathematics represents a curriculum
which requires high expectations of students on behalf of school staff in addition to the outside
IMPROVING ACHIEVEMENT IN MATHEMATICS
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assessments for measuring student achievement as offered. The continuum of aligned, rigorous
curriculum in addition to the external exams makes IB an excellent option for schools to
implement.
In addition, the impact upon students who enroll or complete the IBDP indicates strong
academic results. In a 2001 article, John Gehring referred to IBDP as “The ‘Cadillac’ of College
Prep Programs” for its holistic educational philosophy and curriculum (p. 19). Gamoran (1987)
identified that “Perceiving oneself to be in a college-preparatory program is clearly associated
with higher achievement, even when prior achievement and other background variables, school
setting, composition, and offerings are controlled” (p.149). Of all school subjects, this perception
impacts the content area of mathematics most for gains in achievement (Gamoran, 1987). The
Educational Policy Improvement Center (EPIC) recently measured the IB mathematics
curriculum against the Knowledge and Skills for University Success (KSUS), which serve as
college-readiness standards, found that “for the 83 KSUS standards only 11 were not aligned to
IB standards” (Conley, 2009, p. 7). This indicates that enrollment in and completion of the IBDP
curriculum for mathematics offers students opportunities to gain the skills for success at a
university level.
The question remains as to the significance of completing the IBDP for students and the
impact that this may have upon post-high school opportunities. In 2000-2001, 58% of all U.S.
students in universities graduated with a bachelor’s degree within six years, however of those
who receive an IB Diploma the graduation rate was 88% (International Baccalaureate
Organization, 2010a). Significant in this data, IBO indicates that this rate remains “consistent for
IB students regardless of whether they attend state or private schools or the socio-economic
status of the student” (International Baccalaureate Organization, 2010a, p. 4). In 2009, 59% of
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students enrolled in IBDP in U.S. schools identified as White/Non-Hispanic, while Hispanic
students represented 12% and Black students represented 10% of the IBDP student population
(International Baccalaureate Organization., 2010b). Similarly, rates of entrance to the IBDP
program for low-income students represented 16% of the total IBDP student population in 2009
(International Baccalaureate Organization, 2010b). Though these students are underrepresented
in the IBDP program, often these are the same students who are overrepresented in low-track
homogenous classrooms for mathematics, thus the option for completing advanced coursework
does not exist for those students. Kao and Thompson (2003) indentified that in the past three
decades, racial and ethnic achievement gaps have narrowed and “…although Black and Hispanic
students are more likely to attend college than ever before, they are more likely to attend a
community college than a 4-year institution” (p. 435). With the success rate of university
graduation of IBDP students, if more students of color or low-income backgrounds enrolled and
completed the IBDP it is likely that they would see improvement in entrance and completion of
prestigious university degrees.The data regarding the success of IBDP students indicates that all
students benefit in significant ways, and improve their opportunities for university acceptance
and success. Yet, discrepancies in equity among various groups of students remain an issue to be
addressed.
An example of a school system which addressed this inequity in order to create change is
found in a study by Burris et al. in 2008. The results of one school system were measured,
specifically as all students enrolled in heterogeneous classrooms and completed an IBDP. These
public schools in New York began grouping students heterogeneously in middle school and early
years of high school in an effort to improve achievement of all students. The results of Burris et
al. (2008) study show that “As the school progressively detracked [heterogeneous grouping] the
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ninth and tenth grades, enrollment in eleventh and twelfth-grade IB courses grew, allowing a
majority of students to participate in the program” (p. 582). In a school with 20% of the 1,200
student population identified as African American or Latino and 12% of students identified as
eligible for free/reduced lunch (Burris et al., 2008) the fact that the majority of students enrolled
in IBDP coursework is significant. Implications for Black, Latino, and low-income students are
an increase in equity through opportunities to enroll and complete advanced mathematics
coursework. In the same study, Burris et al. (2008) also found that heterogeneous grouping of
students improved achievement levels for all groups of students as measured by the attainment of
the New York Regents Diploma. This Regents diploma represents coursework beyond the
minimal state graduation requirements and thus signifies the completion of advanced
coursework. Finally, this study showed that students in heterogeneous cohorts had 75% greater
odds of completing IB coursework to obtain the IBDP than the tracked cohorts (Burris et al.,
2008). This benefit of heterogeneous cohorts increasing the chances of completing the IBDP
requirements for a diploma remained true across all scholastic aptitude (as measured by PSAT
scores) levels assessed (Burris et al., 2008). This indicates that more students from all levels of
prior achievement have greater opportunity to enroll and complete the IBDP. Though Burris et
al. (2008) do not conclude that simply eliminating homogeneous grouping will improve
achievement levels, they emphasize values and commitment to students by identifying “Within
the district there were shifts in beliefs, curriculum, pedagogy, and school culture, changes that
accompanied the mechanics of detracking and that educators at the school have seen as essential
to growth in both Regents and IB diplomas” (p.600). These various elements of values and
commitment to students associated with detracking are the same as those which the IBO
succeeds in developing and mandating as schools adopt the IBDP program (Burris et al., 2008).
IMPROVING ACHIEVEMENT IN MATHEMATICS
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These elements indicate that the IBDP provides the continued rigor and equitable opportunity for
students to complete coursework in mathematics for excellent achievement and results.
Thus, the formation of heterogeneous groups of students in mathematics courses entails a
potential shift in values, beliefs, and expectations on the part of school staff. In addition to this,
the current challenge in mathematics remains in preparing students for those high levels of rigor
and achievement early in their school careers in order to give them the opportunity to enroll in
advanced mathematics coursework such as IBDP courses and to receive the IB Diploma. This
starts with schools setting the expectation and offering equitable opportunities for all students to
complete algebra before the end of middle school. Heterogeneous grouping practices paired with
rigorous and constant high leveled curriculum for all students in mathematics indicates that all
students achieve at higher levels. Schools must seriously consider making these changes now, in
order to help students improve achievement in the future.
Conclusion
Students in the United States show via various national and international assessments that
high achievement in mathematics remains a major challenge. A strong understanding of the
content area of algebra must improve as it is essential to opportunities for advanced mathematics
coursework in high-school and university preparedness. Traditionally, students in the United
States given the opportunity to take Algebra courses in 8th grade are considered advanced, highachieving, or gifted, yet research reviewed here indicates that this homogeneous grouping does
not in fact help these students. Additionally, the homogenous grouping hinders many other
students placed in lower tracks of mathematics and keeps achievement levels low. The argument
for heterogeneous grouping of students in middle school must be considered if equity and
IMPROVING ACHIEVEMENT IN MATHEMATICS
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achievement are a focus of education in the United States. Various studies (Burris et al,
2008;Gamoran, 1987; Slavin, 1990; Wheelock, 1992) have shown that strong curricula for all
students in heterogeneous settings results in greater number of students from all prior levels of
achievement improving achievement levels.
However, schools cannot simply stop at offering heterogeneous courses in mathematics
in middle school and hope that students begin to achieve at higher-levels. A shift in expectations,
values, and commitment to students’ achievement must be a priority. In addition, to continue to
improve achievement outcomes such as national and international assessments, high-school
graduation rates, and university entrance and completion, schools must continue to offer rigorous
mathematics coursework throughout high-school. The IBDP represents one example of a
popular, and rapidly expanding advanced curricula within the United States which exhibits the
traits necessary for all students to complete the continuum of rigorous mathematics. Student
access to this program within the United States is higher than in any other country in the world,
and all students must be given the opportunity to take advantage of it. Though challenges exist in
aligning and implementing this continuum as suggested, additional examples of research are also
necessary to show the effects of heterogeneous grouping in middle school paired with the
completion of 8th grade Algebra and the IBDP in high-school. This curricular plan for
mathematics may represent the best opportunity with what already exists within public schools in
the United States to help raise mathematical achievement and potentially close the achievement
which is still present today.
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References
Burris, C.C., Heubert, J. , & Levin, H. (2006). Accelerating mathematics achievement using
heterogeneous grouping. American Educational Research Journal, 43,105-136.
Burris, C.C, Wiley, E., Welner, K., & Murphy, J. (2008). Accountability, rigor, and detracking:
Achievement effects of embracing a challenging curriculum as a universal good for all
students. Teachers College Record. 110, 571-607.
Campbell, P. (2009). IB schools of Georgia. Retrieved from
http://www.fultonschools.org/teacher/bradleyj2/IB/PDF/IBGeorgiaSep09.pdf
Conley, D. (2009) Summary brief: International baccalaureate standards development and
alignment project. Retrieved from Educational Policy Improvement Center
https://www.epiconline.org/files/pdf/IB_Final_Summary.pdf
Gamoran, A. (1987). The stratification of high school learning opportunities. Sociology of
Education. 60, 135-155.
Gehring, J. (2001). The international baccalaureate: ‘Cadillac’ of college-prep programs.
Education Week, 20, 19.
Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., and Brenwald, S. (2008).
Highlights From TIMSS 2007: Mathematics and Science Achievement of U.S. Fourthand Eighth-Grade Students in an International Context (NCES 2009-001). National
Center for Education Statistics, Institute of Education Sciences, U.S. Department of
Education. Washington, DC.
Heubert, J., & Hauser, R. (Eds.). (1999). High Stakes testing for tracking, promotion, and
graduation. National Academy Press. Retrieved from www.nap.edu/catalog/6336.html
International Baccalaureate Organization . (n.d.) The IB diploma programme. Retrieved from
http://ibo.org/diploma/
IMPROVING ACHIEVEMENT IN MATHEMATICS
20
International Baccalaureate Organization. (2011) Statistical Bulletin. Retrieved from
http://www.ibo.org/facts/statbulletin/dpstats/documents/statistical_bulletin_may_2011.pdf
International Baccalaureate Organization (2010a). IB diploma programme: A strong predictor of
success in university. Retrieved from http://ibo.org/recognition/resources/recognize
diploma/documents/StudentPerfBrochure1.9.pdf
International Baccalaureate Organization. (2010b). United States country profile. Retrieved from
http://www.ibo.org/iba/countryprofiles/documents/UnitedStatesCountryProfile.pdf
Kao, G. & Thompson, J. (2003). Racial and ethnic stratification in educational achievement and
attainment. Annual Review of Sociology, 29, 417-442.
Loveless, T. (1998). The tracking and ability grouping debate. Retrieved from
http://challengebychoice.files.wordpress.com/2008/02/the-history-of-tracking.pdf
National Assessment for Educational Progress (NAEP). (2011). Mathematics. Retrieved from
http://nces.ed.gov/nationsreportcard/pdf/main2011/2012458.pdf
Organization for Economic Cooperation and Development (OECD). (2006). Assessing scientific,
reading and mathematical literacy: A framework for PISA 2006. Paris.
Organization for Economic Cooperation and Development (OECD). (2010). PISA 2009 results:
What Students Know and Can Do – Student Performance in Reading, Mathematics and
Science. Retrieved from http://dx.doi.org/10.1787/9789264091450-en
Provasnick, S., & Gonzales, P. (2009). U.S. performance across international assessments of
student achievement. [Supplemental material to The Condition of Education 2009].
National Center for Educational Statistics. Retrieved from
http://nces.ed.gov/pubs2009/2009083.pdf
IMPROVING ACHIEVEMENT IN MATHEMATICS
21
Slavin, R. (1990). Achievement effects of ability grouping in secondary schools: A best-evidence
synthesis. Review of Educational Research, 60, 471-499.
Wheelock, A. (1992). The case for untracking. Educational Leadership, 50, 6.